3x(5x-2)=2x(4x+9)

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Solution for 3x(5x-2)=2x(4x+9) equation: 


Simplifying
3x(5x + -2) = 2x(4x + 9)

Reorder the terms:
3x(-2 + 5x) = 2x(4x + 9)
(-2 * 3x + 5x * 3x) = 2x(4x + 9)
(-6x + 15x2) = 2x(4x + 9)

Reorder the terms:
-6x + 15x2 = 2x(9 + 4x)
-6x + 15x2 = (9 * 2x + 4x * 2x)
-6x + 15x2 = (18x + 8x2)

Solving
-6x + 15x2 = 18x + 8x2

Solving for variable 'x'.

Reorder the terms:
-6x + -18x + 15x2 + -8x2 = 18x + 8x2 + -18x + -8x2

Combine like terms: -6x + -18x = -24x
-24x + 15x2 + -8x2 = 18x + 8x2 + -18x + -8x2

Combine like terms: 15x2 + -8x2 = 7x2
-24x + 7x2 = 18x + 8x2 + -18x + -8x2

Reorder the terms:
-24x + 7x2 = 18x + -18x + 8x2 + -8x2

Combine like terms: 18x + -18x = 0
-24x + 7x2 = 0 + 8x2 + -8x2
-24x + 7x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-24x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + 7x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-24 + 7x)' equal to zero and attempt to solve:

Simplifying
-24 + 7x = 0

Solving
-24 + 7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '24' to each side of the equation.
-24 + 24 + 7x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 7x = 0 + 24
7x = 0 + 24

Combine like terms: 0 + 24 = 24
7x = 24

Divide each side by '7'.
x = 3.428571429

Simplifying
x = 3.428571429
Solution
x = {0, 3.428571429}

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